Pith Number

pith:PLY6ZPXD

pith:2000:PLY6ZPXDDIMXU3JDKB3DRV4HUX

not attested not anchored not stored refs pending

On the approximation of the values of exponential function and logarithm by algebraic numbers

M. Waldschmidt (Paris), Yu. Nesterenko (Moscow)

arxiv:math/0002047 v1 · 2000-02-07 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PLY6ZPXDDIMXU3JDKB3DRV4HUX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Integer points close to a transcendental curve: an algorithmic approach

Receipt and verification

First computed	2026-07-04T14:34:15.506292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7af1ecbee31a197a6d23507638d787a5e1e1cd0a7726cfa2898fa230511e6f20

Aliases

arxiv: math/0002047 · arxiv_version: math/0002047v1 · doi: 10.48550/arxiv.math/0002047 · pith_short_12: PLY6ZPXDDIMX · pith_short_16: PLY6ZPXDDIMXU3JD · pith_short_8: PLY6ZPXD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PLY6ZPXDDIMXU3JDKB3DRV4HUX \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7af1ecbee31a197a6d23507638d787a5e1e1cd0a7726cfa2898fa230511e6f20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1569cb97e54a5bbdbe164f0eb07812adab68ebfcea362ca0f83c9443377848e8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2000-02-07T06:20:32Z",
    "title_canon_sha256": "c7c715a2cb4109cfb597fbedd0b81f53849d6995704875e4ec75f0daaa6be225"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0002047",
    "kind": "arxiv",
    "version": 1
  }
}